I was getting an overview from the documentation, and was wondering how difficult it would be to write a simple debugger.

A novice question -

1) As a project goal, would it be possible to have just the client (using JDI written)? Does the JVM distro come with a well documented back end. What I am trying to say here is, can I simply start a JVM and directly connect to it using an arbitrary front-end? This seems 'true' intuitively, however, just wanted to get it verified.

2) Is there enough documentation to make this as a feasible part-time exercise?

It is easy to write a simple debugger using jdi. There is enough documentation available and also sample
code is available for free. jdk is open source I would suggest you to take a look at the jdb source code.
Please take a look at the jdi documentation and then look at jdb source code.